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Chapter 30
Liquid pressure and
thrust. Centres of pressure
Pressure in liquids
When a ¯uid is in equilibrium the stress across any surface in it is normal to the surface and the pressure intensity at any point of a ¯uid at rest is the same in all directions. The pressure intensity in a homogeneous liquid at rest under gravity increases uniformly with depth. i.e.
where
and
P w g D
P Pressure intensity
w Density of the liquid,
g Acceleration due to gravity, D Depth below the surface.
Total Thrust and Resultant Thrust
If the thrust on each element of area of a surface immersed in a ¯uid is found, the scalar sum of all such thrusts is called the `Total Thrust' whilst their vector sum is called the `Resultant Thrust'. When the surface is plane then the Total Thrust is equal to the Resultant Thrust.
To ®nd the Resultant Thrust
In Figure 30.1, G represents the centroid of an area which is immersed, though not necessarily vertical, in a liquid, and Z represents the depth of the centroid of the area below the surface. Let w be the mass density of the liquid. If an element (dA) of the area, whose centroid is Z1 below the surface, is considered, then:
Thrust on the element dA Pressure intensity Area w g Z1 dA
